
where \(\bar{z}_k\)  is the updated measurement (using Equation REF ), and each \(\mathcal {N} \left( \mu _i, \Sigma _i \right)\)  represents a distinct Gaussian distribution, and \(w_i\)  is the weight for component \(i\) . The problem with a sum-mixture is that the MLE solution is no longer simple and falls outside the common NLLS optimization approaches. We instead consider the max-marginal, leading to the following max-mixture formulation [1]}:
\(p(\bar{z}_k|X) &= \max _{i=1:N} w_i \mathcal {N}\left( \mu _i, \Sigma _i \right)\) 
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